Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20276175 | C2 | semidirect |
| 2. #20276173 | C2 | semidirect |
| 3. #20276114 | C2 | semidirect |
| 5. #20275502 | C2 | semidirect |
| 6. #20274471 | C2 | semidirect |
| 7. C53×#2069 | C2 | semidirect |
| 93. #2069 | D53 | semidirect |
| 114. C53 | #30237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276175 | 2 |
| #20276173 | 2 |
| #20276114 | 2 |
| #20275622 | 2 |
| #20275502 | 2 |
| #20274471 | 2 |
| C53×#2069 | 2 |
| #30237 | 53 |